Problem: Simplify the following expression: $ p = \dfrac{8n - 9}{n + 2} - \dfrac{10}{3} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{8n - 9}{n + 2} \times \dfrac{3}{3} = \dfrac{24n - 27}{3n + 6} $ Multiply the second expression by $\dfrac{n + 2}{n + 2}$ $ \dfrac{10}{3} \times \dfrac{n + 2}{n + 2} = \dfrac{10n + 20}{3n + 6} $ Therefore $ p = \dfrac{24n - 27}{3n + 6} - \dfrac{10n + 20}{3n + 6} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{24n - 27 - (10n + 20) }{3n + 6} $ Distribute the negative sign: $p = \dfrac{24n - 27 - 10n - 20}{3n + 6}$ $p = \dfrac{14n - 47}{3n + 6}$